Let's compare that theory with the facts. Every time Peter preached the gospel in Acts he always spoke of the resurrection of Christ.
Acts 2:
"Men of Israel, listen to this: Jesus of Nazareth was a man accredited by God to you by miracles, wonders and signs, which God did among you through him, as you yourselves know. This man was handed over to you by God’s set purpose and foreknowledge; and you, with the help of wicked men, put him to death by nailing him to the cross. But God raised him from the dead, freeing him from the agony of death, because it was impossible for death to keep its hold on him. David said about him: "‘I saw the Lord always before me. Because he is at my right hand, I will not be shaken. Therefore my heart is glad and my tongue rejoices; my body also will live in hope, because you will not abandon me to the grave, nor will you let your Holy One see decay. You have made known to me the paths of life; you will fill me with joy in your presence.’
"Brothers, I can tell you confidently that the patriarch David died and was buried, and his tomb is here to this day. But he was a prophet and knew that God had promised him on oath that he would place one of his descendants on his throne. Seeing what was ahead, he spoke of the resurrection of the Christ, that he was not abandoned to the grave, nor did his body see decay. God has raised this Jesus to life, and we are all witnesses of the fact. Exalted to the right hand of God, he has received from the Father the promised Holy Spirit and has poured out what you now see and hear. For David did not ascend to heaven, and yet he said, "‘The Lord said to my Lord: "Sit at my right hand until I make your enemies a footstol for your feet." ‘
"Therefore let all Israel be assured of this: God has made this Jesus, whom you crucified, both Lord and Christ."
Acts 3
The God of Abraham, Isaac and Jacob, the God of our fathers, has glorified his servant Jesus. You handed him over to be killed, and you disowned him before Pilate, though he had decided to let him go. You disowned the Holy and Righteous One and asked that a murderer be released to you. You killed the author of life, but God raised him from the dead. We are witnesses of this.
Acts 4
Then Peter, filled with the Holy Spirit, said to them: "Rulers and elders of the people! If we are being called to account today for an act of kindness shown to a cripple and are asked how he was healed, then know this, you and all the people of Israel: It is by the name of Jesus Christ of Nazareth, whom you crucified but whom God raised from the dead, that this man stands before you healed. He is "‘the stone you builders rejected, which has become the capstone.' Salvation is found in no one else, for there is no other name under heaven given to men by which we must be saved."
Acts 10
You know the message God sent to the people of Israel, telling the good news of peace through Jesus Christ, who is Lord of all. You know what has happened throughout Judea, beginning in Galilee after the baptism that John preached— how God anointed Jesus of Nazareth with the Holy Spirit and power, and how he went around doing good and healing all who were under the power of the devil, because God was with him. We are witnesses of everything he did in the country of the Jews and in Jerusalem. They killed him by hanging him on a tree, but God raised him from the dead on the third day and caused him to be seen. He was not seen by all the people, but by witnesses whom God had already chosen— by us who ate and drank with him after he rose from the dead. He commanded us to preach to the people and to testify that he is the one whom God appointed as judge of the living and the dead. All the prophets testify about him that everyone who believes in him receives forgiveness of sins through his name."
There's no significant difference between what Peter preached above and what Paul preached.
So there!
Every time Peter used the death of Christ, have you noticed he is accusing his Jewish listeners of murder?
And when he talks about the resurrection, he is using that, not to tell his listeners that they are now forever justified in the eyes of God, but rather, as proof the Jesus is indeed the Son of God and promised messiah.
I don't know about you but that is significantly very different from Paul preached under the Gospel of grace, which is the cross is something to be celebrated, to boast about. Paul wrote numerous times in his letters to the Gentile Church
Romans 3:25 (NLT) For God presented Jesus as the sacrifice for sin. People are made right with God when they believe that Jesus sacrificed his life, shedding his blood. This sacrifice shows that God was being fair when he held back and did not punish those who sinned in times past
1 Corinthians 1:18 New Living Translation (NLT) 18 The message of the cross is foolish to those who are headed for destruction! But we who are being saved know it is the very power of God.
Galatians 6:4 New Living Translation (NLT) As for me, may I never boast about anything except the cross of our Lord Jesus Christ.
Colossians 1:20 (NASB) and through Him to reconcile all things to Himself, having made peace through the blood of His cross; through Him, I say, whether things on earth or things in heaven.
Colossians 2:14 (NIRV) He wiped out the written Law with its rules. The Law was against us. It opposed us. He took it away and nailed it to the cross.
However, I am saying that Peter was not preaching the same gospel of grace as the Apostle Paul did. As an example, I can imagine if Peter did preach the same message about the cross as Paul did, and if he did mentioned Colossians 2:14. his Jewish listeners would very likely stone him on the spot, given how zealous they are for the law. (
Acts 21:20)
But he didn't have to preach that since Galatians 2 clearly stated
7 But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter;
8 (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles
9 And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.
In the Gospel of the Kingdom, which is for the circumcised Jews, there is no need for them to believe that Jesus died for their sins and rose again as a sign that they are now justified in the eyes of God.
All they need to do is to acknowledge that Jesus is the promised Messiah and King sent to them. As the Gospel of John concluded in ch 20, remember he was one of the 3 apostles who agreed to confine their ministry to only the Jews,
29 Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed.
30 And many other signs truly did Jesus in the presence of his disciples, which are not written in this book:
31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.